Terrorism instills fear in the minds of people and takes away the freedom of individuals to act as they will. Terrorism has turned out to be an international menace today. Here, we study the terrorist attack incidents which occurred in the last half-century across the globe from the open source, Global Terrorism Database, and develop a view on their spatio-temporal dynamics. We construct a complex network of global terrorism and study its growth dynamics, along with the statistical properties of the anti-social network, which are quite intriguing. Normally, each nation pursues its own vision of international security based upon its mandate and particular notions of politics and its policies to counter the threat of terrorism that could naturally include the use of tactical measures and strategic negotiations, or even physical power. We study the network resilience against targeted attacks and random failures, which could guide the counterterrorist outfits in designing strategies to fight terrorism. We then use a disparity filter method to isolate backbone of the network, and identify the terror hubs and vulnerable motifs of global terrorism. We also examine evolution of the hubs and motifs in a few exemplary cases like Afghanistan, Colombia, India, Israel, Pakistan and the United Kingdom. The dynamics of the terror hubs and the vulnerable motifs that we discover in the network backbone turn out to be very significant, and may provide deep insight on their formations and spreading, and thereby help in contending terrorism or framing public policies that can check their spread.